■414 



Mr. W. Grant on the Conjugate Positions 



In order, then, to trace a curve which would represent this 

 path, it was necessary to find several points in it whose posi- 

 tions could afterwards he accurately laid down. This was 

 done by fixing the secondary coil in several positions succes- 

 sively and determining the position of a certain point in it 

 with relation to certain fixed objects, by measurements which 

 were afterwards used as abscissas and ordinates in tracing the 

 curve. These measurements were taken in inches ; and their 

 values are given in the annexed Table, where the columns 

 headed x and y are those of abscissas and ordinates respec- 

 tively. 



*. 



y> 



X. 



jr. 



0-625 



40 



4o 



7-5 



1-0 



4-19 



5-0 



812 



1-5 



4-56 



5-5 



8-75 



20 



5-0 



60 



937 



25 



5o 



65 ' 



10-0 



30 



5-94 



70 



1062 



3-5 



6-44 



7-5 



11-25 



40 



7-0 



8-0 



11-87 



No special arrangement was used to adjust the parallelism 

 of the coils, and only one measurement was taken for each 

 number ; hence the irregularity in the increase of the ordi- 

 nates. The point whose position was determined in each case 

 was the centre of the plane of the secondary coil ; and that is 

 the point which is situated in the curve when silence is main- 

 tained in the telephone. 



The curve (PL XII.) is that found in this way ; and it repre- 

 sents the path which the selected point of the coil has to follow 

 in order that silence may be maintained in the telephone. Ci 

 and C 2 are sections of the primary and secondary coils respec- 

 tively ; C 2 and C u 2 represent the secondary coil in two other 

 conjugate positions. The lines A, A and P, P represent the 

 axis and plane of the primary coil. The points a, b, c, &c. 

 are the intersections of the abscissas and ordinates, and repre- 

 sent the successive positions occupied by the selected point of 

 the secondary coil when the measurements were taken by 

 means of which the curve was traced. As the coils became 

 further separated, however, the position of the curve became 

 less distinct ; and so no attempt was made to trace it further. 



If, now, we suppose the curve to rotate round the axis of 

 the primary coil, a surface will be generated of which it is a 

 section ; and if we observe the conditions necessary for placing 

 the secondary coil in the curve in the proper position for 

 silence, we may place it in any part of the surface with a like 

 result. 



The reason whv we are enabled to trace a curve in this way 



